# Algebra: A Classical Approach

All of the book chapters below are in PDF format for your convenience. They are for use and download by any of my students.

**Chapter 1: The Basics**

1.1 – Integers

1.2 – Rational Numbers

1.3 – Order of Operations

1.4 – Variable Expressions

1.5 – Set Notation

Answers to the Exercises

**Chapter 2: Linear Equations, Absolute Values and Inequalities**

2.1 – Introduction to Equations

2.2 – General Equations

2.3 – Applications of Equations

2.4 – Linear Inequalities and Interval Notation

2.5 – Absolute Value Equations and Inequalities

Answers to the Exercises

**Chapter 3: Polynomials**

3.1 – Exponents

3.2 – Scientific Notation

3.3 – Introduction to Polynomials

3.4 – Multiplying Polynomials

3.5 – Dividing Polynomials

3.6 – Synthetic Division

Answers to the Exercises

**Chapter 4: Factoring**

4.1 – Common Factors

4.2 – Factoring by Grouping

4.3 – Factoring x^2 + bx + c

4.4 – Factoring ax^2 +bx + c

4.5 – Factoring Binomials

4.6 – General Factoring Strategy

4.7 – Solving Equations

4.8 – Applications of Polynomials

Answers to the Exercises

**Chapter 5: Rational Expressions**

5.1 – Simplifying Rational Expressions

5.2 – Multiplying and Dividing Rational Expressions

5.3 – Adding and Subtracting Rational Expressions

5.4 – Adding and Subtracting Rational Expressions with Unlike Denominators

5.5 – Complex Fractions

5.6 – Rational Equations

5.7 – Literal Equations

5.8 – Applications of Rationals

Answers to the Exercises

**Chapter 6: Linear Equations in Two Variables**

6.1 – The Rectangular Coordinate System

6.2 – Graphing Lines by Intercepts

6.3 – Slope of a Line

6.4 – Linear Inequalities

6.5 – Equations of Lines

6.6 – Parallel and Perpendicular Lines

Answers to the Exercises

**Chapter 7: Systems of Linear Equations**

7.1 – Solving Systems of Equations by Graphing

7.2 – Solving Systems of Equations by Substitution

7.3 – Solving Systems of Equations by Elimination

7.4 – Applications of Linear Systems

7.5 – Systems of Linear Inequalities

Answers to the Exercises

**Chapter 8: Radicals**

8.1 – The Principal n-th Root

8.2 – Simplifying Radicals

8.3 – Addition and Subtraction of Radicals

8.4 – Multiplication of Radicals

8.5 – Division of Radicals

8.6 – The Complex Number System

8.7 – Solving Radical Equations

Answers to the Exercises

**Chapter R: Transition and Review**

R.1 – Equations

R.2 – Inequalities and Interval Notation

R.3 – Absolute Values

R.4 – Polynomials

R.5 – Rational Expressions and Equations

R.6 – Radical Expressions and Equations

R.7 – Further Topics in Factoring

Answers to the Exercises

**Chapter 9: Functions**

9.1 – Linear Equations in Two Variables

9.2 – Introduction to Functions

9.3 – Graphing Functions by Plotting Points, Domain and Range of Functions

9.4 – Graphing by Shifting, Reflecting and Dilation

9.5 – Piecewise Defined Functions

9.6 – The Algebra of Functions

9.7 – Inverse Functions

9.8 – Applications of Functions

Answers to the Exercises

**Chapter 10: Quadratic Equations**

10.1 – Solving Quadratics by Factoring and by Extracting Roots

10.2 – Solving Quadratics by Completing the Square

10.3 – The Quadratic Formula

10.4 – Solving Equations in Quadratic Form, Equations Reducible to Quadratics

10.5 – Graphing Quadratic Functions

10.6 – Applications of Quadratic Equations

10.7 – Polynomial and Rational Inequalities

Answers to the Exercises

**Chapter 11: Exponentials and Logarithms**

11.1 – Exponential Functions

11.2 – Logarithmic Functions

11.3 – Graphing Logarithmic Functions

11.4 – Properties of Logarithms

11.5 – Solving Exponential and Logarithmic Equations

11.6 – Applications of Exponentials and Logarithms

Answers to the Exercises

**Chapter 12: Conic Sections**

12.1 – Distance and Midpoint Formula

12.2 – The Parabola

12.3 – The Circle

12.4 – The Ellipse

12.5 – The Hyperbola

12.6 – Further Topics in Conic Sections

Answers to the Exercises

**Chapter 13: Systems of Equations and Inequalities**

13.1 – 2×2 Systems of Equations Revisited

13.2 – Larger Systems of Equations by Gaussian Elimination

13.3 – Solving Systems using Cramer’s Method

13.4 – Nonlinear Systems of Equations

13.5 – Inequalities of Two Variables

13.6 – Systems of Inequalities of Two Variables

Answers to the Exercises

**Chapter 14: Polynomial and Rational Functions**

14.1 – Polynomial Functions

14.2 – Rational and Irrational Roots of Polynomials

14.3 – Graphing Polynomials

14.4 – Graphing Rational Functions

Answers to the Exercises

**Chapter 15: Sequences and Series**

15.1 – Sequences and Series Basics

15.2 – Arithmetic Sequences and Series

15.3 – Geometric Sequences and Series

15.4 – The Binomial Theorem

Answers to the Exercises